How to pack images into blend file
You can use the Pack All Into .blend function. Open the project, go to File > External Data > Pack All Into .blend, and wait for the packing of your images/textures (it depends on how many textures you used in your project). Then save again the file (maybe with a different name, e.g. project_packed). So when you open the file on a different computer, you don't have to re-loading the textures.